3
N Brockers always active : always able to handle a request (i.e. serve or forward a request to its predecessor) whether it is « local » or not Members are dynamics : join a local colony, stay connected for a while and then leave (temporarily or permanently)

4
Focus on single, atomic*, request R issued at brocker i n at t=0 (brocker i n ancestor of brockers i n-1, …,i o ) X i (t) = membership of colony i at time t T(i) = set of nodes in tree rooted at i * Can be extented

13
Members join each colony according to independent Poisson processes (reasonnable assumption) Intensity i for colony i Each member stays connected for a random time with an arbitrary distribution  i = Mean connection duration in colony i Proposition (membership distribution in colony i) X i ~ Poisson rv with mean  i = i.  i P(X i =k) = (  i ) k exp(-  i )/k!